iPhone crashes during restore

I have an iPhone 5s, bought 14 months ago (without Apple Care, so out of warranty).

Background Information:

Since I updated to iOS 8.1.1, my iPhone has been crashing infrequently, in: Blue screen, Apple logo, back to blue screen, Apple logo, etc. This would solve itself after an hour or two (sometimes more), and the phone would then be useable again.

However, even though it would take a long time sometimes, eventually the phone would crash again. I went to my local Apple Premium Reseller (iCentre Delft, the Netherlands), and they said I should restore the phone via iTunes. I did and it worked fine for approximately 5 days. But then, this morning, it crashed again. Same thing as before. But this time it DID NOT go back to usable, and I decided to try and hook it up to iTunes again. It wasn't recognized, however, and therefore I could not restore my phone. I called Apple Support, and they said I should put the phone into recovery (DFU) mode. I did, and it clearly shows the iTunes logo with the lightning cable. But now comes the problem:

The problem:

When I connect to iTunes, I get the normal messages requesting me to reset the phone (2). It starts just fine, but when the first white appears on the bar on the iPhone, it gets stuck (while the bar in iTunes keeps moving). 10 seconds later, and the blue screen pops up again, after which it heads back to the basic recovery mode screen. On iTunes I get error 9, which shows USB connection issues. However, I doubt that this is the case and suspect that it gives this error because it has nothing else to give.

Does anybody have any suggestions?